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Copper and iron conductors current ratio

Short answer

At 20°C resistances are equal. At 100°C: R_copper = 1.336R, R_iron = 1.480R. Since parallel voltage is same, current division is inverse: I_copper/I_iron = 1.480/1.336 = 1.108. Copper carries 52.6% and iron 47.4% of total current.

Two conductors, one of copper and the other of iron are connected in parallel and at 20°C carry equal currents. What proportion of current will pass through each, if the temperature is raised to 100 °C? Assume temperature coefficient of resistance at 20 °C for copper as 0.0042 per °C and for iron as 0.006 per °C.

Two conductors in parallel have the same voltage across them, so the currents divide in inverse ratio of their resistances: I₁/I₂ = R₂/R₁.

Step 1: Equal currents at 20°C

Equal currents at the same voltage means equal resistances at 20°C. Let R_cu = R_fe = R at 20°C.

Step 2: Resistances at 100°C

R_cu = R [1 + 0.0042 × (100 − 20)] = R × 1.336 R_fe = R [1 + 0.006 × (100 − 20)] = R × 1.480

Step 3: Current division

I_cu/I_fe = R_fe/R_cu = 1.480/1.336 = 1.108

Fraction through copper = 1.480/(1.336 + 1.480) = 0.5256 Fraction through iron = 1.336/(1.336 + 1.480) = 0.4744

Answer: Copper carries about 52.6 % and iron about 47.4 % of the total current (ratio 1.108 : 1).

✓ Answer checked by Claude Opus 5.5 (high effort)

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